Coherence of quantum channels

Abstract

We investigate the coherence of quantum channels using the Choi-Jamiołkowski isomorphism. The relation between the coherence and the purity of the channel respects a duality relation. It characterizes the allowed values of coherence when the channel has certain purity. This duality has been depicted via the Coherence-Purity (Co-Pu) diagrams. In particular, we study the quantum coherence of the unital and non-unital qubit channels and find out the allowed region of coherence for a fixed purity. We also study coherence of different incoherent channels, namely, incoherent operation (IO), strictly incoherent operation (SIO), physical incoherent operation (PIO) etc. Interestingly, we find that the allowed region for different incoherent operations maintain the relation $PIO\subset SIO\subset IO$. In fact, we find that if PIOs are coherence preserving operations (CPO), its coherence is zero otherwise it has unit coherence and unit purity. Interestingly, different kinds of qubit channels can be distinguished using the Co-Pu diagram. The unital channels generally do not create coherence whereas some nonunital can. All coherence breaking channels are shown to have zero coherence, whereas, this is not usually true for entanglement breaking channels. It turns out that the coherence preserving qubit channels have unit coherence. Although the coherence of the Choi matrix of the incoherent channels might have finite values, its subsystem contains no coherence. This indicates that the incoherent channels can either be unital or nonunital under some conditions.

11 pages, 7 figures. One result concerning Holevo quantity has been removed

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• Maximum Relative Entropy of Coherence for Quantum Channels
• Skew information-based coherence generating power of quantum channels
• Improvement in quantum communication using quantum switch
• The resource theory of coherence for quantum channels
• Quantumness of channels
• An alternative framework for quantifying coherence of quantum channels
• Quantifying coherence of quantum channels based on the generalized $\alpha$-$z$-relative Rényi entropy
• On coherence of quantum operations by using Choi-Jamiołkowski isomorphism
• Coherence dynamics induced by attenuation and amplification Gaussian channels
• Creation of quantum coherence with general measurement processes
• Experimental verification of a coherence factorization law for quantum states
• Coherence monotones of quantum channels based on two generalized quantum relative entropies